A Very Debated Topic

[Tony]

This question has caused numerous debates on GameFAQs. Most if not all of them get really heated. This is the question that is posed: Does .9 repeating equal 1?

I say it does not. I will post my reasons why later when others have answered.

[Temanin]

This question strikes debate? The word "equal" makes this a mute point, as no, .999 repeating is not the exact same thing as 1. Mathematically speaking, anyway. In normal application, .999 repeating is usually treated as 1, and in finding limits, an answer of .999 repeating normally represents the answer 1. But I'm rambling. No, they are not equal.

Cheers.

[Faceless]

Have to agree with Tem, it's doesn't equal one. If people say it "equals" one, they're rounding it, and rounding is not the same thing as equaling.

[Faceless]

Anyone else have anything to add?
If not, what are your reasons Tony, or are they the same as already mentioned.

[Tony]

The difference may be so infinitely small, but it's there. And it separates the two numbers. Just like the probability that life would evolve from a few cells to become multicellular organisms that create nuclear weapons that threaten all life.

But that's off topic. The Algebra II/Programming teacher at my school says otherwise. But then, he's from an older generation. I mean, he use to be able to read punch cards for computers, for Christ's sake. He's old and his math is flawed. But since he's old he thinks he is right, so there is no point in arguing with him.

[Temanin]

Well, using algebra, there is a way to "prove" that .999 repeating equals 1, technically. But algebra has a few flaws in it. For instance, the definite integral from -1 to 2 of 1/x^2, using simple algebra, is 1/2. But in fact, the answer is something like 3.5 (I can't remember the exact answer at the moment and don't feel like doing the problem again), since algebra doesn't take into consideration discontinuity and non-differentiable points, just to name a few.

It's just quite silly, in all actuality. You can also prove that 2=1 using the inherent flaws in algebra.

[Tony]

I saw that equation. And that 2=4 or 3. I forgot which.

I should point that out to the teacher. Can you specifically name the flaws so I can prove him wrong?

[Temanin]

Well, they're not really set flaws that you can write down. They're just inherent mistakes that occur in random problems and procedures. Sadly.

[Tony]

Damn. Oh well. I guess he will continue to follow his flawed Algerbra.

[Metzgermeister]

In case we've not decided on whether .99 repeating = 1 yet, imo no. Think of it like if you just kept 1/2ing a number, you'd never, ever, hit 0.